Definition:Bounded Metric Space/Definition 4
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Definition
Let $M = \struct {A, d}$ be a metric space.
Let $M' = \struct {B, d_B}$ be a subspace of $M$.
Let $a' \in A$.
$M'$ is bounded (in $M$) if and only if:
- $\exists K \in \R: \forall x \in B: \map {d} {x, a'} \le K$
Also see
Sources
- 1997: Christian Berg: Metriske rum: $\S 1.3$